Foundations of Mathematics

Mathematical and Formal Logic

What are logical operators in truth tables?

Logical operators in truth tables include such words as “and” or “or,” which are all represented by certain symbols (for more about logical operators in predicate calculus, see below). For example, “and” (also called the conjunction operator) is also referred to as a binary operator. It is one of the most useful logical operators, as in “p AND q”, represented by the symbols ∧ or &. The “or” (also called the disjunction operator) is also a binary operator, as in “p OR q”, and represented by the symbols Image and |. The “not” (also called the negation or inversion) operator is known as a unary operator, and is represented by the symbols ˜ or Image (in computer programming, NOT is often represented by the !). The “implies” (or implication operator) is also a binary operator; its symbols include ∴, ⊃, and Ã.

But note: Not all logical operators seem to represent words the way we are accustomed to using them, and many times they seem to contradict their proper definitions. But in a truth table, the logical operator means what it means—without the usual nuances of the English language.


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